Pythagorean Theorem

Today in class we studied the Pythagorean theorem. It is named after the Greek mathematician and philosopher Pythagoras and describes the relationship between the lengths of sides of a right triangle.

The Pythagorean theorem states that for every right triangle a2 + b2 = c2 where a and b are lengths of the of the legs of the triangle and c is the hypotenuse (longest side). The theorem allows you to find a missing side of a right triangle or show that a triangle is a right triangle. In order to use the theorem you simply put the values that you know into the theorem and solve for the missing variable.

Example: A right triangle has legs of 3 and 4. What is its hypotenuse?
a2 + b2 = c2
32 + 42 = c2
9 + 16 = c2
25 = c2
5 = c

A common use of the Pythagorean theorem is to create right angles. By choosing three lengths that satisfy the theorem exactly like 3, 4, and 5, the triangle must be a right triangle. This helps make sure projects are square. Pythagorean triples (whole numbers that satisfy the theorem exactly) are used in many ways in construction to make walls square during, lay out a tile floor, or any application that requires precise right angles.

I found this interesting way to generate all of the Pythagorean triples. Suppose that m and n are two positive integers, with m < n. Then n2 - m2, 2mn, and n2 + m2 is a Pythagorean triple.

This link describes the process further and gives a list of triples - Generating triples